Certain attempts at distributed cryptographic operation, such as signing and encrypting/decrypting, are known. However, no previous system enjoys efficiency of operation combined with high level of security and availability in a system that retains its security while any minority of distributed servers collude and stop, misbehave, and try to help in breaking the system's secret. Other attempts have been made to deal with various issues of threshold cryptography and mobile adversaries, although only a limited number discuss proactive function sharing.
The notion of "proactive public-key" was addressed in A. Herzberg, S. Jarecki, H. Krawczyk, and M. Yung in: Proactive Secret Sharing, or: How to Cope with Perpetual Leakage, Advances in Cryptology--Crypto 95 Proceedings, Lecture Notes in Computer Science, Vol. 963, D. Coppersmith ed., Springer-Verlag, 1995, pp. 339-352 ("[HJKY]"). This implementation was based on "discrete logarithm" with exponentiation in a prime field (i.e., given the elements modulo a prime p, use a generator of GF(q) where q divides p-1). This problem involves distributed computation over keys, and the keys in this case are taken from domains whose algebraic structure is public (a group of a known order).
A number of other theoretic references to making cryptographic mechanisms proactive include: R. Ostrovsky and M. Yung, How to Withstand Mobile Virus Attacks, Proc. of the 10th ACM Symposium on the Principles in Distributed Computing, 1991, pp. 51-61 ("[OY]"); R. Cannetti and A. Herzberg, On Maintaining Security in the Presence of Transient Faults, Advances in Cryptology, Proc. of Crypto '94 ("[CH]"); A. Herzberg, M. Jakobsson, S. Jarecki, H. Krawczyk, and M. Yung, Proactive Public Key and Signature Systems, The 4-th ACM Symp. on Comp. and Comm. Security, April 1997 ("[HJJKY]"); Y. Frankel, P. Gemmel, P. MacKenzie and M. Yung, Proactive RSA, Tech Report Version SAND96-0856, Sandia National Laboratories, March 1996 ("[FGMY]"). Each of the references cited above, and all other references cited below, are fully incorporated herein by reference.